Priest is an odd duck. He illustrates the problem of combining two disparate
enterprises: the pursuit of logic as a pure formal enterprise (in his case paraconsistent
logic, which admits of true contradictions, whose attendant doctrine is dialetheism),
and the substantive engagement with philosophical issues and ultimately the
real world. While logic was practically developed to study the nature of inference,
valid and invalid argument (without larger philosophical claims), its formal
form has never neatly meshed with the messiness of the real world nor with the
structuring the categories of its fundamental understanding. Furthermore, mixing
up logic with metaphysics has, historically, more often served the cause of
mysticism than science.

In his 1995 (with additions in 2002) book Beyond the Limits of Thought,
Priest bravely reviews the history of western philosophy (with Nagarjuna thrown
in in 2002) and attempts to unify all paradoxes in his Inclosure
Schema. Paradoxically, paradoxically, by the time he has accomplished this
task, he has left the philosophical content of all these philosophies embodying
these paradoxes behind. In other words, the bare formal structure he seeks to
generalize does not do justice to the nature of the philosophical issues involved.

In a later paper on philosophy in the 21st century, Priest predicts that Asian
philosophy will be the next big thing. Perhaps this ties in to his interest
in Nagarjuna, Taoism, and the martial arts. About Marxism he seems to throw
up his hands and suggest that somehow it drowned in the Sea of Ilyenkov. I'll
review this article more extensively at a later date.

However, back in 1989, Priest aggressively attempts to prove that Hegel, Marx,
and Engels were adherents of dialetheism. What this amounts to may prove instructive.

(1) That Hegel's dialectics is dialetheism should be a no-brainer, Priest argues.
Hegel states that the very nature of motion embodies contradiction. (You will
be familiar with the issue from Zeno's paradox.) But others have denied that
Hegel affirms contradiction in the formal logical sense.

Marxist philosophers have made similar denials about the Marxist view of dialectical
contradiction. Sometimes contradiction is characterized as the co-existence
of conflicting forces, which is hardly a logical interpretation. Priest cites
a few to that effect. After the Stalin era (in which contradiction hazily covered
a variety of meanings), a growing number of Soviet philosophers dissociated
the notion of dialectical contradiction from any taint of logical contradiction
(Sheptulin, Narskii), and some maintain that contradictions hold in thought
but not in reality (Narskii).

(2) The arguments against this position: In Hegel's time, the only logic extant
was Aristotle's logic, which Hegel deemed inadequate from a dialectical perspective.
But Frege/Russell logic is far more sophisticated, and is the gold standard
now. Contradiction is even more taboo. Note Priest's quotation of Popper on
dialectic. Most Marxists, who know little of formal logic, have been browbeaten
into retreating from dialetheism. But now we have paraconsistent logic to the
rescue.

(3) Dialetheic logic: Priest outlines the principles of paraconsistent logic,
which may assign truth values of both true and false. He also discusses its
semantics. He also introduces an operator ^ to nomialize sentences, e.g. ^A
means "that A" (e.g. 'that Sam went to the store' is true). Further
discussion.

(4) Motion: an illustration. Priest claims that paraconsistent logic can easily
render Hegel's notion of the paradox of motion into logical form. He also deals
with an argument based on a distinction between extensional and intensional
contradiction. In extensional contradiction, there is no intrinsic connection
between the conjuncts. But for intensional (putatively dialectical) contradictions,
there is an internal relation between the conjuncts not captured by a mere extensional
conjunction (A & not-A). Priest treats this latter qualification by way
of example (with reference to Grice's conversational implicature), but leaves
us hanging, and promises to pick up the argument again in section 8.

(5) The history of Hegel's dialectic: This section is quite interesting, and
appears to be remote from the realm of paraconsistent logic. Hegel draw on his
predecessors Kant and Fichte as well as the medieval Neo-Platonists who held
that the One embodies contradictions. Priest quotes Hegel's analysis of Kant's
antinomies of reason. Hegel objects to Kant's banishing contradiction from the
world and relegating it to the Reason claiming that "reason falls into
contradiction only by applying the categories". The postulation of the
not-ego by the ego as argued by Fichte is also summarized. Art the end of this
review, Priest claims to have firmly established Hegel as a dialetheist.

(6) Contradiction in Hegel's dialectic: There is a lengthy treatment of Hegel's
view of Geist, with reference to Fichte, that segues into the master/slave
dialectic and Sartre's notion of freedom. Then Priest takes up the argument
that all these 'contradictions' do not refer to the same thing in the same respect,
which he considers a dodge. (In his later book he calls this parameterization.)

(7) Contradiction in Marx's dialectics: In his youthful Feuerbachian phase,
Marx transmutes Hegel's geist into Humanity and takes up the theme of alienated
labor and self-development. Priest briefly characterizes the structural logic
at work here. Then he skips to the mature Marx, on use-value and exchange-value,
and the forces and relations of production.

Then he moves on to Engels, who states his views more plainly. We are back
to the contradiction of motion. While impatient with the tendency to abuse Engels,
Priest concedes that Engels saw contradiction where it doesn't exist, e.g. in
his infamous claim about the square root of minus one.

(8) Identity in difference: Hegel's notion is for Priest the essential form
of dialectical contradiction. Here Priest translates Hegel's argument about
the identity of opposites into logical notation. The only example cited is the
paradox of motion.

Priest thinks he has proved his case, as promised in section 4. Now if my abstract
of the overall argument seems disjointed, this is just how I see the original.
There is a schizoid tendency plainly evident to me that escapes Priest's attention:

(a) Priest qua logician can talk about logic;

(b) Priest is capable of discussing the substance of philosophical doctrines;

(c) yet, when he attempts to combine the two, he is a complete idiot. Mixing
up the metaphysician in him and the logician yields only the most philistine
product: the logician superficially wins out by trivially rendering some formal
property in logical notation, totally evading the substantive philosophical
content in the zeal to prove that A and not-A are simultaneously predicated.
This is neither fish nor fowl, merely a foul fish or a fishy foul. To paraphrase
Lenny Bruce, this is so obtuse, it's thrilling.

(9) Dialectics and epistemology: Priest admits that there is much more to dialectics
than these formal considerations, i.e the analysis of concrete contradictory
situations. He takes up the example of being-in-itself and being-in-consciousness.
He then contrasts the positions of dualists (Locke), non-dialectical monists:
idealists (Berkeley), traditional materialists (cf. central state materialism).
Presumably, the dialectical monist resolves this conundrum. True to form (pun
intended), Priest illustrates the resolution with logical notation. Miraculously,
he fails to see the triviality of such a treatment, as he fails to illuminate
any of the ideas involved, nor does he add anything by using the symbols c and
not-c.

(10) Conclusion: Priest's bête noir is the pussyfooting around in fear
of acknowledging a contradiction. Priest indeed concludes with the statement
that his paper at least calls a spade a spade. (There seems to be a subtle Tarskian
allusion here. It would have been more obviousand funnier!if he
wrote: "a 'spade' is a spade" iff a 'spade' is a spade.)

It is truly remarkable that such sophisticated means should be marshalled to
such an unsophisticated end. It is also most telling that throughout the essay
Priest favorably refers to Sean Sayers, with whom he even shared a draft of
his paper. He also references this debate, published in a book:

My long-term readers will recognize this title and recall that I wrote an exhaustive
analysis of this debate in the mid-'90s.
Very briefly: Sayers took the most philistine position, defending the most intellectually
sloppy version of dialectical materialism (clogged up with fudge on the nature
of logic, which even the Soviets abandoned after the Stalin era), adding further
offense by citing Mao. Norman defends Engels' general effort to formulate a
nonreductive materialism while criticizing his logical confusions and Sayers'
shoddy reasonings. But there was never a Maoist anywhere who was not a moron,
and Norman's analysis fell on deaf ears (or blind eyes). That Priest could embrace
Sayers as he does is truly a prodigious feat for a logician. Here we have an
example of not only the troubled relation between logic and reality, but the
vexed relation between their intermediaryphilosophyand logic. Logic
as a self-contained formal enterprise is one thing; engagement with philosophical
issues another, and the reality beyond yet something else. Aside from the historical
fact that philosophy and logic were done by the same people (in China and India
as well as in what is called the West), in my opinion they make very poor bedfellows.

While I don't expect everyone to be held spellbound by this question, it is
illustrative of a recurring problem in intellectual history (and also in popular
intellectual culture, which is another story. Priest's views on dialetheism
(logic which admits contradictions) is controversial among his fellow logicians,
and he responds to objections in his book. Probably his fellow logicians (except
those interested in Marx, among which there are more than a few) are not terribly
concerned about his views on Marx, and in fact he says nothing about Marx in
his book. However he did get a response to his earlier article on dialectics
and dialetheism:

Marquit himself is a Marxist (and a physicist, I believe) who maintains that
logical contradictions are unacceptable. Priest counters this by reaffirming
the existence of formal logics not susceptible to this limitation. Moreover,
Marquit is wrong to claim that contradiction is intolerable in theoretical investigations,
citing Dirac's early formulation of quantum mechanics and teh early infinitesimal
calculus as examples. However, as all theories get replaced eventually, inconsistencies
or no, one can't argue much on this basis. (Am I missing something, or is Priest
undermining himself here?)

Then there is Marquit's argument as to the difference between idealism and
materialism. While Hegel's idealism requires an identity of opposites, materialism
does not. Priest argues that the substantive differences between Hegel and Marx
are irrelevant to the question of whether the entities in question have formally
contradictory properties. Marquit argues that a succession of states in time
(state A and state not-A) are contradictory or not depending on whether Hegel's
or Marx's logical and historical dialectics are temporal or not. I'm not going
to reproduce the confusing paragraph in question, but suffice it to say that
Priest counters this argument. Finally, Priest claims that since Marx says that
he took over his dialectic from Hegel, we should take his word for it, along
with the criticisms he explicitly makes of Hegel's dialectic. Oy!

In his earlier article, Priest cites three alleged examples of Marx's dialetheism;
Marquit addresses only one, with the familiar ploy of reinterpreting a situation
in which A & not-A are both true as being so in different respects.
The example in question is a famous one from Marx on the nature of the commodity,
its use value, exchange value, and equivalency. Priest analyzes this example
from Capital as well as another one from A Contribution to Political
Economy to counter Marquit's argument.

Priest segues to the contradictory nature of wage labor, both free and unfree.
Here too he counters Marquit's attempt to weasel out of a contradiction in the
same respect.

Next Priest discusses the nature of motion, beginning with Zeno's paradox.
Here I am confused about Priest's argument about the unsatisfactoriness of the
Russellian argument, about which he claims to agree with Marquit. Then he throws
quantum mechanics into the mix, and I can't make sense out of the argument anymore,
as we move into paragraphs on the uncertainty principle and the two-slit experiment.
Priest concludes that he is not "suggesting that quantum mechanical descriptions
are descriptions of an inconsistent reality. My point is just that it is premature
to claim quantum mechanics as an ally against dialetheism."

I don't know whether you can make any sense out of my summary of this article,
but to me the article itself is an awful mess. I offer a few observations:

(1) Priest treats disparate examples as if they are alike:

(a) . . . the nature of motion (implying, firstly, the nature of the continuum).
There is a philosophical dimension, a scientific dimension, and a mathematical
dimension to this problem. The ancient Greeks, lacking the calculus (though
I'm told that Archimedes came close), could not handle the mathematical dimension,
but they dealt with both the logical (philosophical) and scientific dimension
of the problem as best they could. The strictly logical dimensioni.e.
the nature of the continuuminvolves the question of infinite divisibility
of the line into points. If I remember correctly, already Aristotle challenged
Zeno by denying that motion should be considered as a succession of states of
rest, and that the line, while potentially infinitely divisible, should not
be considered as a collection of points (or actual infinity of real numbers,
a nondenumerable infinite set as Cantor proved it to be).

Then there is the relation between the mathematical idealization and the physical.
In his book Priest recounts Aristotle's struggle with the concept of the atom
on the one hand and on the other the (im)possibility of the physical infinite
divisibility of matter and space. This is already an issue more than two millennia
before the worse problems introduced by quantum mechanics. Curiously, in this
article, Priest acknowledges that quantum mechanics complicated matters, but
otherwise remains simplistic in his indifference toward other distinctions.

Interestingly, Marx had a hobby in the last decade of his life, writing about
the various explanations of the calculus in the old textbooks he read and evaluating
their relative (in)adequacies. These manuscripts have been published and analyzed.
(I think they were analyzed before they were published.) Priest does not mention
them or compare them to other treatments, such as those of Engels. While I do
vaguely recall Dirk Struik's treatment of Marx's analysis of three approaches
to the calculus (all before Weierstrauss et al straightened out the mess), I
don't recall Marx making any of the claims or arguments that Engels does (Van
Heijenoort exonerates Marx of the intellectual sins he finds in Engels),
let alone linking them in any way to his social theory.

(b) . . . the nature of the commodity and the money economy: how do the alleged
contradictions here relate in any way to the nature of the continuum? True,
motion in time as well as space also involves a measurement along the continuum,
and thus raises the question of nature of the "instant" (both at rest
and in motion?), but how does this abstract property of the time continuum relate
to Marx's social theory and substantive critique of political economy? There
is an abstract question of the viewpoint of stasis vs. that of motion (development),
but can it be stated as baldly identical to the apparent paradox of the continuum
(of time)? We can continue to argue philosophically over the nature of the instant
and whether motion should or should not be considered as a succession of states
of rest, or rather, inversely, that the paradox emerges from the artifact of
freezing motion as hypothetical point-instants. But in the meanwhile we do have
the calculus to address the question mathematically. We even now have nonstandard
analysis. What analog do we have in approaching the relation of use-value and
exchange-value according to Marx? (OK, Marx used math in his critique of political
economy, but is this some sort of axiomatizable theory?) How is it possible
to switch from one example to the other as if one is engaging an identical argument
in both cases?

(c) . . . freedom and unfreedom: here we have a categorial pair far removed
from the nature of the continuum and simple physical motion, and no math to
resort to. The mutual (dialectical) interrelation of these categories, or other
pairs (indeterminism-determinism, chance-necessity, freedom-necessity) raises
a whole different question from that of the nature of motion and the continuum.
Priest briefly addresses the question of internal relations in his previous
essay, which as far as I can tell just gets lost even where he promises to nail
it. Priest is so obsessed with showing that A & not-A are both predicated
in all of his examples, he fails to note not only their substantive differences
but whether or not this formula tells us anything meaningful about the relation
of A and not-A, or about the examples in question.

(2) Is there any meaningful way that paraconsistent logic can be applied to
illuminate any higher-level philosophical questions, or for that matter the
nature of use-value and exchange-value according to Marx? What is the point
of such an exercise? Does it add anything to our understanding of the matter
at hand, or does it even formally capture its logical structure?

(3) Priest's argumentation is truly remarkable to me. One would think that
as a person versed in both contemporary formal logic (unlike the average Marxist)
and Hegel and Marx (unlike the average logician or analytical philosopher) that
he would escape the recurrent pattern of simplistic arguments. Yet, for all
his delving into substantive philosophical ideas and theories, all he cares
about in the end is validating dialetheism, i.e. establishing the existence
of formal contradictions, just as if he were another simpleton regurgitating
the bad arguments of Stalinists, Trotskyists, and Maoists, his more sophisticated
qualifications notwithstanding. What does Dr. Paraconsistency have to offer
in relation to the contributions of Ilyenkov, Zelený, Tony Smith, Uno,
Arthur, and scores of others? Where is the synthesis of the achievements of
modern logic and analytical philosophy and the Hegelian-Marxist heritage? All
I got was this lousy T-shirt.

11 September 2005

Postscript (response to complaint)

My review is part of a much larger project, which has to do with
the relation of logic and reality, and beyond that, the fragmentation of knowledge
under conditions of alienation. That would be the "Marxist" angle
that interests me, rather than advocacy of 'Marxism' per se. Graham Priest is
far more interesting than Sean Sayers was at the time of the debate in question.
But let's review the logic of my intervention.

Priest's book (1995, 2002) Beyond the Limits of Thought doesn't mention
Marx or Marxism, though Hegel emerges as the hero of the book. We also know
from Priest's earlier two essays in Science and Society that he is a
Marxist or has a keen interest in Marxism. Furthermore, he is one of those rare
individuals in the English-speaking world with an interest in both dialectics
and formal logic. So it is important to see how he seeks to unite the two. But
oddlyand this part of my larger purviewhe doesn't seem to have a
whoe lot to say about dialectics (or about the vcarious philosophies he treats
later) except to make his one big pitch for paraconsistent logic which offers
a formalism for incorporating contradictions. But what good is this formalism
in terms of modeling reality in a substantive fashion? I can't tell. And this,
it seems to me, Priest merely reproduces the conditions of alienated theoretical
labor and fails to overcome fragmentation and to unify an understanding of how
logic relates to other philosophical issues and to objective reality itself.
His grasp of formal logic should make him far more sophisticated than the dialectical
materialists of old, but he seems bent on making the same trivial points.

15 September 2005

Erwin Marquit's articles in Science and Society offset the two articles
by Graham Priest previously described.

Marquit (1981) endeavors to clarify the three 'laws of dialectics' beginning
with a formulation of what he calls "law zero", the law of universal
interconnection. He then clarifies the logic of the famed three laws and their
relation one to one another. His next step is to clarify objective and subjective
dialectics and their relation to one another. Taking examples of antinomial
statements which seem to embody logical contradictions, Marquit then argues
that dialectical contradictions are not logical contradictions. (319). Examples
chosen from Hegel, Engels, and quantum mechanics can be expressed in the form:
"A changing object exists in a given state and not in the given state at
the same time." Other views are brought in from Ilyenkov, F.F. Vyakkerev,
Gottfired Stiehler, and D.P. Gorskii. Marquit's main inspiration is Igor S.
Narski.

While I have not really described Marquit's argument, I will give him credit
for treating this matter in an uncommonly precise and sophisticated manner,
which Priest (the logician!) unaccountably shortchanges. I don't recall what
I've seen by Narski, though I am familiar with the name. Also in evidence is
the increasing professionalism and sophistication of Soviet philosophers following
the death of Stalin.

Marquit details the treatment by Hegel and Engels of dialectical contradictions
as logical contradictions. Marquit claims that materialist dialectics, in contradistinction
to idealist dialectics, "dialectical negation is embodied by the unity
of the historical and the logical." (152) "Hegel's need for the identity
of opposites is made clear by his insistence that one must begin with the identity
of pure being and pure nothing " (154) and is tied up with the changeability
of essence. But materialist dialectics "starts from differentiated being".
Marquit treats of an example from quantum mechanics, and returns to Zeno's paradox
(the clearest case offered by Engels). The paradox arises from viewing motion
as a succession of stopped states. While this is a necessary procedure of analysis,
we must recognize that the paradox arises from just this cognitive act. (157)
Both Hegel and Lenin recognized this problem. Marquit then returns to another
example from quantum mechanics, and explains how the dialectical contradiction
does not yield a logical contradiction. (158-9)

Marquit then criticizes Priest (1989/90) and takes up the noted example of
Marx's 20 yards of linen, then proceeds to other examples. Marquit then criticizes
Sean Sayers, and suggests that Marxists have barely begun to elaborate the dialectical
character of major scientific and mathematical breakthroughs (163). Marquit
then turns to Ilyenkov, who tends to avoid any postulation of logical contradictions
and who provides a much subtler analysis than Priest. (163-5)

The upshot, I think, is that even if Priest can prove Marquit wrong in arguing
for contradictions in 'the same respect', that one point does not render his
analysis of the issues involved any subtler, nor does it lead to interesting
arguments and conclusions. The argument is to one point onlythe admission
of contradictions into formal logic. And so?